An apparatus of this type is known from German Pat. No. DE-PS 29 09 803. After start of the internal combustion engine, the apparatus of this type has the problem that the respective adjusting piston travels at high speed into a maximum adjustment position and repeatedly impacts there at significant generation of noise. The reason for this is the fact that after shutdown of the internal combustion engine, hydraulic fluid residing in the apparatus gradually escapes from there so that the adjusting piston is no longer sufficiently supported, whereby, normally, a certain residual volume of hydraulic fluid is retained. As a consequence of the irregular rotation of the camshaft, the adjusting piston is shifted, after re-starting the internal combustion engine, into an end position under the mentioned significant noise development, because the adjusting piston is no longer hydraulically supported. This condition is observed during the period between ignition of the internal combustion engine and charging of the pressure compartments, i.e. few seconds after start of the engine.